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loop,I B current has
I
time rate of
S
dt a
S
a
(center 2 N
of
dBx S
coil, inducing
BI
S
eop
29.1–29.6.) conductor: thatmagnetic proportional to r. The magnetic
B
0 NI
B
nitude
is inversely z a current has a mag dB
2ExamplesB = mExample 28.6.)
8.3
Ox
S
current in the coil.
change of
S
(28.17)
long, straight conductor carryingmagnetic Iﬂux through the loop. This relationx
S
multiB
IB
PSu
N
S
I
e law
N
m2aI d l : r ﬁeld lines are circles is validwith r. Thethe withBdirecx is caused by a
S
0
ship coaxial whether magnetic
B
nitude that is inversely proportional to the wire, ﬂux change
I
dP
S
S
dB
(28.6) righthand rule. (See S S
r
(center of N circular loops)given by the
Examples 28.3
CHAPTERtionsare circles changing magnetic ﬁeld, direcdBxof the loop, or both.
ted by
B
B
2ﬁeld lines
4p
S
coaxial with the wire, dB motion
with
r
dB
and 28.4.)
S
S
e ﬁeld
Ampere’s law: Ampere’srighthand rule. (See line integral 0
^
f
tions given by the law states that the ExamplesdB 5
rS
(See Examples 29.1–29.6.)28.3 A B d l = m0 Iencl
(28.20)
S
m0 II ¿ S
F
rs:
S
r law:
I
I
S
S
of B around induced current equals m0 times S B Axis of d
the net curand 28.4.)
z’sfrom Lenz’s law states that anany closed path or emf alwaysI tendsLto oppose lor cancel out
=
(28.11)
Change in B
B0
r du B
S
tract if 948 2pr through the area
S
ya
S
d
r
S
f
CHAPTER 28can be derivedMagnetic dB 5 TheBpositive
Field S l S S
ntegral that causedrentLenz’s lawMagnetic enclosed byFaraday’s law andconductors:
change L B dSFaraday’s law: Sources of betweenthe path.the induced B easier to F d £ ¿
it. m I
from currentcarrying Fis often
use. m0 II
S
I
B
l = 0 encl
(28.20)
force
S
S
Faraday’s law states thatI F
emf
I
B
S
A
duB
the
=
(28.11)
SI
d
L
dS
l
B
(increasing)
net cureB
Examples 29.7 and 29.8.) current is determined currentcarrying conductorsBattract ifE =  2pr
(29.3)
sense of
rthe timer rate of
Two long, parallel, by a righthand rule.S(See
B
L m II ¿
S
SS
S
in a closed loop equals the negative of r conductors:
orce
B
dt
2.)
ISS BF
Magnetic force between the same direction and ddu f if the F
currentcarrying
B
B
0
dB
I
ositive
I
S
Examples 28.7–28.10.) are in
the
I
I
FL
E
The
S
B
u
n their
changedue long,currents currentcarrying conductors magnetic ﬁelds caused by several current(28.11)
of to currentﬂux through the loop. ThisSrepel if L = 2pr
distributions: The table dlists attract
distributions. In each case the con magnet’s
S
parallel,
r
dl
e. (See Magnetic ﬁeldsTwo magneticare in oppositelaw: Lenz’s law relation an induced current or emf always tends to oppose or cancelFout B otion causes a
SS
currents
m
S
Lenz’s directions. The magnetic that
I I NS B
B states force
S
tion of
S
validper unit the same direction and repel if the
whether
ductor isship isthe current Iare in theﬂux change isBcausedSby a on their
carrying currents . length between the conductors depends
I
F
Binduced
948
CHAPTER 28 Sources of Magnetic Field B it. Lenz’s law can be derived from Faraday’...
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 Spring '14
 Magnetic Field, Lenz

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